All categories

4 years ago

Find the root of the quadratic equation y=3x^2-30x+45

1 answer:

4 0

$y=3x^2-30x+45\\\\a=3;\ b=-30;\ c=45\\\Delta=b^2-4ac\\\\\Delta=(-30)^2-4\cdot3\cdot45=900-540=360 \ \textgreater \ 0\\\\therefore\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{360}=\sqrt{36\cdot10}=\sqrt{36}\cdot\sqrt{10}=6\sqrt{10}\\\\x_1=\dfrac{30-6\sqrt{10}}{2\cdot3}=\dfrac{30-6\sqrt{10}}{6}=\boxed{5-\sqrt{10}}\\\\x_2=\dfrac{30+6\sqrt{10}}{2\cdot3}=\dfrac{30+6\sqrt{10}}{6}=\boxed{5+\sqrt{10}}$

You might be interested in

√₂

snow_lady [41]

Answer:

$2000 was invested at 5% and $5000 was invested at 8%.

Step-by-step explanation:

Assuming the interest is simple interest.

<u>Simple Interest Formula</u>

I = Prt

where:

I = interest earned.
P = principal invested.
r = interest rate (in decimal form).
t = time (in years).

Given:

Total P = $7000
P₁ = principal invested at 5%
P₂ = principal invested at 8%
Total interest = $500
r₁ = 5% = 0.05
r₂ = 8% = 0.08
t = 1 year

Create two equations from the given information:

$\textsf{Equation 1}: \quad \sf P_1+P_2=7000$

$\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500$

Rewrite Equation 1 to make P₁ the subject:

$\implies \sf P_1=7000-P_2$

Substitute this into Equation 2 and solve for P₂:

$\implies \sf 0.05(7000-P_2)+0.08P_2=500$

$\implies \sf 350-0.05P_2+0.08P_2=500$

$\implies \sf 0.03P_2=150$

$\implies \sf P_2=\dfrac{150}{0.03}$

$\implies \sf P_2=5000$

Substitute the found value of P₂ into Equation 1 and solve for P₁:

$\implies \sf P_1+5000=7000$

$\implies \sf P_1=7000-5000$

$\implies \sf P_1 = 2000$

$2000 was invested at 5% and $5000 was invested at 8%.

Learn more about simple interest here:

brainly.com/question/27743947

brainly.com/question/28350785

5 0

1 year ago

Christov and Mateus gave out candy to children on Halloween. They each have out candy at a constant rate, and they both gave awa

padilas [110]

Answer: 1) Both gave same number of candies to each child.

2) Christov gave candy to a greater number of children.

Step-by-step explanation:

Since, Christov initially had 300 pieces of candy, and after he was visited by 17 children, he had 249 pieces left.

Let he gave x candy to each student when he visited 17 children.

Then, 17 x + 249 = 300

⇒ 17 x = 51

⇒ x = 3

Since, he distributes candies in a constant speed.

Therefore, his speed of distribution = 3 candies per child

Now,The function that shows the remaining number of candies Mateus has after distributing candies to n children,

C(n)=270 - 3 n

Initially, n = 0

C(0) = 270

⇒ Mateus has initial number of candies = 270

When he gave candies to one child then remaining candies = 270 - 3 × 1 = 267

Thus, the candies, get by a child from Mateus = 270 - 267 = 3

Since, he distributes candies in a constant speed.

⇒ His speed of distribution = 3 candies per child

1) Therefore, Both Christov and Mateus have same speed of distribution.

2) Since, both have same seed.

⇒ The one who has greater number of candies will be distribute more.

⇒ Christov will give more candies.

8 0

4 years ago

NEED HELP ASAP:

zepelin [54]

Answer:

2035.8 (approximately)

6 0

4 years ago

Read 2 more answers

I’m so confused please help there’s a photo above btw

Strike441 [17]

Wow I don't get it either but my guess would be 9,6...sorry....

8 0

4 years ago

Read 2 more answers

A football team loses an average of 3 yards per play. How many yards

Minchanka [31]

The expression would be:

x=number of plays

Insert 4:

3(4)

=12

They would 12 yards after 4 plays if losing 3 yards every play.

5 0

3 years ago